Any disease that is considered life threatening should disqualify imo.
Isn't this why there are underpresidents? And after that, Head Law? There's a whole list, I think. If they're thought to be the best for the job, even if their holding of that job is going to be small, they should have the chance to do it.
Any mental instability issues should disqualify a candidate for presidency.
Donald Trump has cognitive dissonance, please disqualify.
Besides brain illness being often hard to mean and subjective, this could potentially be wielded just to shut up folk in brain illness healing buildings that are "out of politic liking".